Abstract: Creation of scalar massless particles in two-dimensional Minkowski
space-time--as predicted by the dynamical Casimir effect--is studied for the
case of a semitransparent mirror initially at rest, then accelerating for some
finite time, along a trajectory that simulates a black hole collapse (defined
by Walker, and Carlitz and Willey), and finally moving with constant velocity.
When the reflection and transmission coefficients are those in the model
proposed by Barton, Calogeracos, and Nicolaevici [$r(w)=-iα/(\w+iα)$
and $s(w)=\w/(\w+iα)$, with $α\geq 0$], the Bogoliubov coefficients
on the back side of the mirror can be computed exactly. This allows us to prove
that, when $α$ is very large (case of an ideal, perfectly reflecting
mirror) a thermal emission of scalar massless particles obeying Bose-Einstein
statistics is radiated from the mirror (a black body radiation), in accordance
with results previously obtained in the literature. However, when $α$ is
finite (semitransparent mirror, a physically realistic situation) the striking
result is obtained that the thermal emission of scalar massless particles obeys
Fermi-Dirac statistics. We also show here that the reverse change of statistics
takes place in a bidimensional fermionic model for massless particles, namely
that the Fermi-Dirac statistics for the completely reflecting situation will
turn into the Bose-Einstein statistics for a partially reflecting, physical
mirror.